Self-regulated reconfigurable resonant voltage/current-mode method and device for extended-range inductive power transmission

ABSTRACT

A current-based resonant power delivery (CRPD) device and method with multi-cycle switching that enables efficient inductive power transmission at large distances. The proposed CRPD switches the Rx LC-tank for several cycles to utilize it as a current source. Therefore, the voltage across the load (R L ) can be significantly higher than the Rx LC-tank voltage. In CRPD, the energy may first be stored in the receiver (Rx) coil by shorting the Rx LC-tank for several power carrier cycles. At the peak of Rx coil current, the coil energy may then be transferred to load (R L ) for a quarter of the power carrier cycle.

REFERENCE TO RELATED APPLICATIONS

This application claims priority from U.S. Provisional Patent Application Ser. Nos. 62/378,364, filed Aug. 23, 2016 and 62/533,832, filed Jul. 18, 2017, the entire content of both of which is incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates to circuitry for use in inductive power transfer systems and, in particular, to a self-regulated reconfigurable resonant voltage/current mode device and method for extended-range inductive power transmission.

BACKGROUND OF THE INVENTION

Inductive power transmission has been used extensively over the past decades for contactless energy transfer to power a device or recharge its battery. It has covered a wide range of applications with different power requirements from μW to kW. Some examples include powering radio frequency identification (RFID) tags and implantable medical devices (IMDs), and recharging batteries of handheld mobile devices and electric vehicles. FIG. 1 shows a generic model of a conventional inductive power transmission link. It includes a rectifier or a voltage multiplier depending on the voltage amplitude across L₂C₂-tank, i.e., V_(R). The power management also includes a regulator (not shown). In an inductive power transmission link, as shown in FIG. 1, an efficient power amplifier (PA) drives the transmitter (Tx) coil, which is mutually coupled to a receiver (Rx) coil. A power management is required to rectify and regulate the AC voltage across the L₂C₂-tank (V_(R)) to a constant DC voltage across the load (R_(L)), i.e., V_(L) in FIG. 1.

In general, there are four key parameters in inductive power transmission: (1) power delivered to the load (PDL), defined as P_(L)=V_(L) ²/R_(L); (2) power transmission efficiency (PTE), defined as P_(L)/P_(S), where P_(S) is the PA output power; (3) power conversion efficiency (PCE) within Rx, defined as P_(L)/P_(R), where P_(R) is the power management input power; and (4) voltage conversion efficiency (VCE) in Rx, defined as V_(L)/V_(R,peak), where V_(R,peak) is the amplitude of V_(R).

While achieving high PTE and sufficient PDL should always be considered in the design of inductive links, maximizing PCE or VCE depends on V_(R). When V_(R) is larger than the required V_(L), which is the case when coupling distance (d) is relatively small and coils are well aligned, high PCE is more desirable to maximize the power efficiency within Rx, and VCE<1 V/V is quite acceptable. However, for V_(R)<V_(L) with large d and/or misaligned coils, VCE>1 V/V is paramount to achieve the required V_(L) even at the cost of lower PCE. Therefore, for most wireless power transmission (WPT) applications that involve d and coil orientation (φ) variations, the power management should be able to sense V_(R) and decide to whether maximize PCE or VCE.

The mutual coupling between a pair of coupled coils, k₁₂, is inversely proportional to d³. A key requirement in all of the aforementioned applications is to provide sufficient V_(L), while maintaining high PTE. In worst-case conditions when d is relatively large, then the coils are misaligned, or the Rx coil is miniaturized. It should also be noted that even in some low-power applications such as neural stimulators, a relatively high V_(L) is often required. In these conditions, one can increase the PA voltage, V_(s), to further increase V_(L). In practice, however, V_(L) can only be increased to the extent that the tissue exposure to the electromagnetic field is maintained within safety limits, and regulatory requirements for interference with nearby electronics are satisfied. Therefore, achieving sufficient V_(L) at large distances is quite challenging.

The PTE of the 2-coil link in FIG. 1 is also highly sensitive to R_(L), which is often given by the application. In order to improve PTE for any R_(L), multi-coil links in the form of 3- and 4-coil links have been proposed that provide load matching inside Rx. However, these links need an additional coil in the Rx, which adds to the size, cost, and complexity of the system. In some applications, R_(L) can change significantly during the operation while 3- and 4-coil links cannot dynamically compensate for R_(L) variations during the system operation. Alternatively, off-chip matching circuits can also be used to transform R_(L). However, a network of off-chip capacitors and inductors is needed to dynamically tune a wide range of R_(L) during the operation, which again adds to the size, cost, and power loss in the Rx. Therefore, the power management should also provide optimal load condition during the operation.

In order to improve the PCE within Rx, active rectifiers with high-speed synchronous comparators, some equipped with delay compensation, have been presented in recent years. A 3-level reconfigurable resonant regulating rectifier simultaneously rectifies and regulates V_(L) by switching between full-bridge, half-bridge, and no rectifier structures. A resonant regulation rectifier may employ pulse-width/frequency modulation to adjust the on-time window of the active rectifier switch for self-regulating V_(L), by controlling the forward current. Although high PCE and self-regulation have been achieved in active rectifiers, they suffer from low VCE<1 V/V due to the voltage drop across the active switch.

In order to improve VCE, voltage doublers, multipliers, and DC-DC converters have been presented in the past. The power-management structure may also be switched between rectifier and doubler for voltage regulation and range extension. Although these techniques can improve VCE, they require additional AC-DC converters and/or off-chip components due to the low-frequency operation of the inductive links (<20 MHz), adding to the size, cost, and power loss in the Rx. A common theme with the aforementioned power managements is that they use the Rx LC-tank as a voltage source, i.e., they operate in voltage mode (VM), inherently leading to limited VCE.

SUMMARY OF THE INVENTION

A current-based resonant power delivery device for inductive power transmission to a load is disclosed herein. In accordance with one embodiment, the device comprise a transmitter coil, a receiver circuit, the receiver circuit having a receiver coil, a resonance capacitor, a switch, a rectification device, and a load capacitor. The transmitter coil is configured to energize the receiver coil. The receiver coil is connected to the load via the resonance capacitor and the rectification device. The switch has a first state and a second state. The receiver circuit is configured to build up and transfer energy between the receiver coil and the resonance capacitor by bypassing the load during the first state of the switch. The receiver circuit is further configured to transfer energy from the receiver coil to the load during the second state of the switch. The rectification device may include a diode.

In some embodiments, the switch remains in the first state for a plurality of power carrier cycles until the receiver coil reaches a desired receiver coil current and then the switch transitions from the first state to the second state, the switch remains in the second state for one-quarter of a power cycle, and returns to the first state for the plurality of power carrier cycles. The switch may have an adjustable switch frequency, and the switch transitions from the first state to the second state and vice versa. In some embodiments, the receiver coil and the resonance capacitor are connected in a series connection, the switch is connected in parallel with the series connection, and the rectification device is connected between the resonance capacitor and the load. In some embodiments, the switch is transitioning between the first state and the second state at a switching frequency to maintain the load about a desired voltage.

A current-based resonant power delivery method for inductive power transmission to a load is also disclosed herein. The method comprise the steps of providing the above-discussed current-based resonant power delivery device, energizing the transmitter coil, selecting the first state of the switch for building up and transferring energy between the receiver coil and the resonance capacitor for a predetermined time and selecting the second state of the switch for transferring energy from the receiver coil to the load after the pre-determined time. Some embodiments in accordance with the method may comprise the steps of connecting the receiver coil and the resonance capacitor to each other in a series connection, connecting the switch in parallel with the series connection, and connecting the rectification device between the capacitor and the load.

A self-regulated resonant voltage/current mode method power delivery device for inductive power transmission to a load is also disclosed herein. In accordance with one embodiment, the device comprise a transmitter coil, a receiver circuit, the receiver circuit has a receiver coil, a resonance capacitor, a first switch, a second switch, a rectification device, and a load capacitor, wherein the transmitter coil is configured to energize the receiver coil. The embodiment also comprise a mode selection circuit operable to select a voltage mode or a current mode based on a voltage across the receiver coil and a desired load voltage across the load, the mode selection circuit selects the voltage mode when the desired load voltage is less than the receiver coil voltage and the mode selection circuit selects the current mode when the desired load voltage is more than the receiver coil voltage.

Furthermore, the receiver coil is connected to the load via the first switch, the first switch is configured to maintain the load about the desired load voltage by employing back current during the voltage mode, the receiver coil is further connected to the load via the resonance capacitor and the rectification diode, wherein the second switch is connected from the resonance capacitor to the ground. The second switch in accordance with the embodiment has a first state and a second state, the receiver circuit is configured to build up and transfer energy between the receiver coil and the resonance capacitor by bypassing the load during the first state of the second switch during the current mode, the receiver circuit is further configured to transfer energy from the receiver coil to the load during the second state of the second switch when a desired energy is stored in the receiver coil during the current mode, and the second switch is configured to maintain the load about the desired load voltage by adjusting its switching frequency during the current mode.

In some embodiments of the self-regulated device, the first switch transitions between an ON state and an OFF state at a first switching frequency. The first switch may employ back current during the ON state. In some self-regulated devices, the second switch transitions between the first state and the second state at a second switching frequency. The receiver coil and the resonance capacitor may be connected in a series connection, the second switch connected in parallel with the series connection, and the rectification device connected between the resonance capacitor and the load. The rectification device may comprise a third switch and the receiver circuit configured to transfer energy from the receiver coil to the load through the third switch during the second state of the second switch. Some embodiments further comprise a voltage mode controller, and the voltage mode controller regulates the first switching frequency to maintain the load about the desired load voltage. Other embodiments further comprise a current mode controller, and the current mode controller regulates the second switching frequency to maintain the load about the desired load voltage.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment (s) of the invention and together with the description serve to explain the principle of the invention. In the drawings:

FIG. 1 shows a generic model of a conventional inductive power transmission link;

FIG. 2 shows the key waveforms for achieving both rectification and regulation in an active rectifier in proposed technique with employing the back current by increasing T_(on);

FIG. 3 is a circuit schematic of an inductive link equipped with current-based resonant power delivery (CRPD) according to one embodiment of the present invention;

FIG. 4 shows a switching diagram and key waveforms of an embodiment of CRPD to achieve high AC-DC VCE (V_(L)/V_(R,peak));

FIG. 5A is an embodiment of a CRPD-based inductive link model with a closed switch (M₁) in accordance with region (I) of FIG. 4;

FIG. 5B shows an embodiment of a CRPD-based inductive link model with an open switch (M₁) in accordance with region (II)-(III) of FIG. 4;

FIG. 6 shows simulated and calculated results for key signals of an embodiment of the CRPD-based inductive link shown in FIG. 4, when M₁ was switched at f_(sw)=50 kHz;

FIG. 7 is a graphical representation of simulated and calculated V_(L) vs. time for an embodiment of a CRPD-based inductive link, when V_(R,peak)was 1 V;

FIG. 8 is a design optimization flowchart for a proposed CRPD-based inductive link;

FIG. 9 is a block diagram of the proposed adaptive reconfigurable VCIPM chip that operates either in VM or CM based on V_(R) amplitude, and can perform rectification, regulation, and OVP all in one step using one off-chip capacitor (C_(L));

FIG. 10A is a schematic diagram and key waveform of a voltage mode controller (VMC) in a VCIPM chip to generate a proper SW₂ pulse;

FIG. 10B is a schematic diagram and key waveform of a current mode controller (CMC) in a VCIPM chip to generate a proper SW₁ pulse;

FIG. 11 is a CRPD measurement setup that includes two PCB coils, a discrete control circuit for L₂C₂-tank switching and power delivery to C_(L)∥R_(L);

FIG. 12A shows measured key waveforms of the proposed CRPD in FIG. 3, operating at f_(p)=1 MHz and f_(sw)=50 kHz to deliver power to the R_(L) of 100 kΩ;

FIG. 12B shows measured key waveforms of the proposed CRPD in FIG. 3, operating at f_(p)=1 MHz and f_(sw)=50 kHz to deliver power to the R_(L) of 100 kΩ. From top: V_(L), V_(R), and SW₁ waveforms, wherein V_(L) increased to ˜3.1 V after ˜30 ms of switching, where |V_(R)| was only 1 V, leading to a VCE of 3.1;

FIG. 13 is a graphical representation of measured V_(L) and PTE of the CRPD-based inductive link vs. f_(sw) for R_(L) of 100 kΩ at d₁₂=7 cm and |V_(s)|=0.39 V;

FIG. 14A is a graphical representation of measured V_(L) of the CRPD-based and conventional inductive links vs. R_(L) at d₁₂=7 cm and |V_(s)|=0.39 V;

FIG. 14B is a graphical representation of measured PTE of the CRPD-based and conventional inductive links vs. R_(L) at d₁₂=7 cm and |V_(s)|=0.39 V;

FIG. 15 is a graphical representation of measured values for V_(L) for the CRPD-based and conventional inductive links vs. d₁₂ for R_(L) of 100 kΩ and |V_(s)|=1.05 V;

FIG. 16 is a graphical representation of measured V_(L) of the CRPD-based and conventional inductive links vs. the amplitude of the received voltage, |V_(R)|, for R_(L) of 100 kΩ, d₁₂ of 7 cm, and f_(sw) of 50 kHz;

FIG. 17 is a VCIPM chip micrograph, occupying 1.56 mm² and 0.52 mm² with and without pads, respectively;

FIG. 18A is a graphical representation of measured V_(L) and V_(R) waveforms in voltage mode (VM) when the Tx voltage (V_(s) in FIG. 9) was increased from 11 V_(p-p) to 15 V_(p-p) at R_(L)=100 kΩ;

FIG. 18B is a graphical representation of Zoomed waveforms for V_(L) and V_(R), demonstrating how back current regulated V_(L) at 3.2 V despite V_(s) variations;

FIG. 19A is a graphical representation of measured V_(L) and V_(R) waveforms in current mode (CM) when V_(s) was increased from 4 V_(p-p) to 9 V_(p-p) at R_(L)=100 kΩ;

FIG. 19B is a graphical representation of zoomed waveforms for V_(L) and V_(R), demonstrating how changes in f_(sw) regulated V_(L) at 3.2 V despite V_(s) variations; and

FIG. 20 is a graphical representation of measured V_(L), V_(R), and V_(s) waveforms when V_(s) was manually increased from 4 V_(p-p) to 10 V_(p-p), resulting in the automatic reconfiguration of the VCIPM chip from CM to VM based on the V_(R) amplitude (1.2 V vs. 3.3 V) to regulate V_(L) at 3.2 V.

DETAILED DESCRIPTION OF THE INVENTION

Reference will now be made in detail to some embodiments of the present invention, examples of which are illustrated in the accompanying drawings. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like parts. Furthermore, it is required that the present invention is understood, not simply by the actual terms used but by the meaning of each term lying within. Additional advantages, objects, and features of the invention will be set forth in part in the description that follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.

I. Introduction

As will be apparent to those skilled in the art that a Rx LC-tank can be used as a current source to overcome the low VCE issue by operating in current mode (CM). In Pennsylvania State University's previous work, called Q-modulation, the Rx LC-tank has been shorted twice in every power carrier period, T_(p)=1/f_(p), to store energy and then deliver it to the load. Although Q-modulation can increase V_(R) and, therefore, PTE and PDL by dynamically transforming relatively small R_(L) (hundreds of ohms) to the optimal load, its VCE is still limited due to the use of a rectifier, and is only suitable for small R_(L) matching.

Using another approach with a modified multi-carrier Q-modulation, the Rx LC-tank may be shorted for several power carrier cycles without any particular timing, to enable Q-modulation at higher power carrier frequencies. However, unlike the original Q-modulation discussed above, the Rx LC-tank switching in this modified method is synchronized with the power carrier, and again, the VCE obtained has been smaller than one.

Also known is a resonant CM battery charger that is used to recharge a battery from sub-volts AC carriers across the Rx LC-tank. However, this power management is not suitable for direct WPT due to its startup issue, and it achieves low PCE for small R_(L) and large V_(R).

Considering a wide range of d, φ, and R_(L) variations in inductive links, therefore, neither VM nor CM power managements can provide the optimal performance. Thus, a reconfigurable voltage/current mode inductive power management (VCIPM) is proposed that can adaptively switch between VM and CM based on V_(R) amplitude to (1) maximize PCE and PTE, when R_(L) is small and V_(R) is larger than the required V_(L) of 3.2 V; and 2) maximize VCE and PTE for large R_(L) and small V_(R)<3.2 V. In the proposed VCIPM chip, V_(R) envelope is first detected and compared with 3.2 V. If V_(R,peak)>3.2 V, VM configuration is selected and the power management operates as an active voltage rectifier with high PCE. If V_(R,peak)<3.2 V, CM configuration is selected.

In CM, a new current-based resonant power delivery (CRPD) technique is utilized with only one single switch to short the series-connected Rx LC-tank of the inductive link for several power carrier cycles in a unique fashion to use it as a current source. Therefore, an AC-DC voltage conversion with high VCE greater than one can be achieved in the Rx side. This can extend the range of inductive power transmission, particularly for applications that involve low-power consumption in the Rx side, or require a large V_(L).

The proposed concept includes a proof-of-concept CRPD technique that is implemented with discrete components. In this measurement, CRPD could achieve high VCE of 3.1 V/V at R_(L)=100 kΩ. It could also improve PTE for large R_(L) (tens of kΩ and above) by transforming R_(L) to the equivalent parallel resistance of the Rx LC-tank, which is typically in the order of several kΩ and below. Section II below discusses the proposed VCIPM concept. The CRPD concept, circuit theory, and modeling is presented in Section III. The optimization of CRPD-based inductive links is discussed in section IV, VCIPM chip architecture is discussed in Section V, followed by proof-of-concept measurements results in Section VI. The following discussion may refer to the references provided subsequent to Conclusion i.e. Section VII.

A VCIPM prototype chip was fabricated in a 0.35 μm 2P4M standard complementary metal-oxide-semiconductor (CMOS) process to prove functionality of the proposed power management. The VCIPM chip regulates V_(L) at a desired level of V_(DD) by controlling the back current in VM and the switching frequency in CM, eliminating the need for the regulator and its associated off-chip capacitor. The VCIPM chip also performs over-voltage protection (OVP) along with self-regulation in VM using back current. Therefore, the VCIPM chip only requires two off-chip capacitors, one for resonance, and one for rectification/regulation/OVP. The VCIPM concept is presented in Section II. A. The VCIPM chip circuit design and measurement results are presented in Sections V and VI, respectively.

II. Proposed VCIPM Concept

The proposed VCIPM operates in either VM or CM based on V_(R) amplitude. For the cases where V_(R) is large enough to reach desired V_(L), VM configuration is chosen to achieve high PCE, otherwise CM is selected to have a functional system. Key operational waveforms in VM are shown in FIG. 2. In VM, SW₁ is high (M₁: ON), and V_(R) across the parallel L₂C₂-tank is rectified with a synchronous active rectifier, formed by the low-dropout M₂ switch and SW₂. According to the conventional approach, on time of an active rectifier is utilized to regulate V_(L) at desired level of V_(DD). This approach encounters serious challenges for conditions where V_(R) or R_(L) is large. Because T_(on) decreases drastically, leading to higher power consumption and larger V_(R) that can damage power management. Thus, conventional structures need another circuit for OVP.

In the proposed VCIPM, back current technique is utilized to solve this problem. As shown in FIG. 2, the proposed technique for rectification, regulation, and OVP—all in one step—employs back current during T_(d) by maintaining M₂ on for longer time periods (larger T_(on)) to allow current to flow from C_(L) to the Rx L₂C₂-tank. In other words, extra energy is turned back from C_(L) to inductor to regulate V_(L). This technique not only increases T_(on), but also maintains V_(R) just slightly above V_(DD) by detuning the L₂C₂-tank with C_(L), when R_(L) is large and/or d and φ are small. Therefore, only one off-chip capacitor (C_(L)) is needed for rectification, regulation, and OVP.

III. Proposed Current-Based Resonant Power Delivery (CRPD) Technique

FIG. 3 shows a circuit schematic of the proposed inductive link, equipped with CRPD. A single switch (M₁) is added to the conventional inductive link to short the L₂C₂-tank for several power carrier cycles, and then deliver L₂C₂-tank energy to the load (C_(L)∥R_(L)), when the Rx coil current (i_(L2)) is at its peak. Compared to the conventional inductive link in FIG. 1, a single switch (M₁) has been added in parallel with the series-connected L₂C₂-tank, and the power management is represented by a passive rectifier to generate a DC voltage (V_(L)) across the load capacitor and resistor (C_(L)∥R_(L)). As shown in FIG. 3, in CRPD the L₂C₂-tank is connected in series, while in conventional inductive links the L₂C₂-tank can be connected in parallel or in series for large and small R_(L) values, respectively.

In some embodiments of the present invention, a switch (M₁) may be connected with a plurality of L₂C₂-tank circuits, such that the plurality of L₂C₂-tank circuits may be energizing a load. One or more L₂C₂-tank circuits may be connected at any moment with the switch (M₁). A L₂C₂-tank circuit may be connected with a plurality of switches (M₁). In some embodiments, a switch may also be connected with energy sources other than a L₂C₂-tank circuit. A switch may be a solid state device such as a transistor, silicon-controlled rectifier, MOSFET, JFET or a triac.

A. CRPD Concept

FIG. 4 shows a switching diagram and key waveforms of the proposed CRPD, including Rx coil current (i_(L2)), V_(R), V_(L), and the clock for controlling the M₁. The M₁ is first closed for several T_(p)s to store energy in the L₂C₂-tank. Then, the M₁ is opened at the peak of i_(L2) for 0.25 T_(p) to deliver L₂C₂-tank energy to the load. The operation of the CRPD may be divided into 3 regions. In region (I), which is shown as t₀<t<t₁ in FIG. 4, the M₁ is closed for several power carrier cycles (T_(p)=1/f_(p)). Therefore, the high-Q L₂C₂-tank stores the energy, provided by the inductive link. In region (II), which is shown as t₁<t<t₂ in FIG. 4, at the peak of i_(L2), i.e., i_(L2,max), where the voltage across C₂ is zero and all the energy is stored in L₂, the M₁ is opened for less than 0.25 T_(p) to deliver all the L₂ energy to the load. At t=t₂, i_(L2) reaches zero and the switching state remains open in region (III), which is shown as t₂<t<t₃ in FIG. 4, for t₃−t₁=0.25 T_(p). At t=t₃ the next power cycle starts, the M₁ is closed again, and i_(L2) starts building up.

The switching timing is key in CRPD, because the L₂C₂-tank should have enough time of several T_(p)s to store a high amount of energy, and the energy transfer to the load needs to be started at i_(L2,max) by opening the M₁ for T_(off)=0.25 T_(p), as shown in FIG. 4. While the onset of turning the M₁ on and off are fixed in the CRPD, its switching frequency, i.e., f_(sw)=1/T_(sw), is a degree of freedom that has been provided by the CRPD, compared with conventional inductive links.

At t=t₁, since V_(R) is zero and the only path for discharging L₂ is the rectifier, V_(R) suddenly increases to >V_(D)+V_(L), where V_(D) represents the forward voltage of the rectifier. The peak voltage of V_(R) in region (I), i.e., V_(R, peak), does not need to be higher than V_(L), because the L₂C₂-tank is being used as a current source. Therefore, an AC-DC voltage conversion with high VCE, may be achieved. Since the L₂C₂-tank is in series with C_(L)∥R_(L) in regions (II) and (III) and C_(L) is much larger than C₂, L₂ may be fairly assumed at resonance in the proposed CRPD according to the present invention. In addition, since the duration of regions (II) and (III) are much shorter than that of region (I), the L₂C₂-tank resonance and quality factor may be approximated to those in region (I).

It should be noted that in CRPD since the Rx LC-tank is shorted for several cycles, during which L₂ cannot deliver power to R_(L), a larger R_(L) value might be used as this demands less power. For applications with a small R_(L), in region (I) where only C_(L) provides power for R_(L), V_(L) decreases significantly and, therefore, the steady-state V_(L) could be smaller than V_(R, peak) in FIG. 4.

B. The Circuit Theory Behind CRPD

FIGS. 5A and 5B show the inductive link model in regions (I) and (II)-(III), respectively, to find i_(L2), V_(L), and PTE. Since the M₁ is open in both regions (II) and (III), the equivalent circuit in FIG. 5A may be used for both regions. The mutual inductance between L₁ and L₂, i.e., M₁₂, may be modeled with V₁₂=−jω_(p)×M₁₂×I_(L2) and V₂₁=jω_(p)×M₁₂×I_(L1) in Tx and Rx sides, where ω_(p)=2π/T_(p)=2πf_(p) is the power carrier frequency, and I_(L1) and I_(L2) are the amplitude of sinusoidal currents in L₁ and L₂, respectively.

As shown in FIG. 5A, the M₁ is closed for a pre-determined period thus disconnecting load R_(L) from the L₂C₂-tank. During the pre-determined period, the energy provided by the inductive link is stored in the L₂C₂-tank. As shown in FIG. 5B, the M₁ is opened after the pre-determined period and the L₂C₂-tank gets connected with load R_(L). Now all the energy stored in the L₂C₂-tank is delivered to load R_(L). FIG. 5B shows a diode and a capacitor i.e. passive rectifier as part of the power management on the load end. Some embodiments according to the present invention may use another power management scheme having a different circuit configuration.

Since the duration of region (I) is much longer than that of regions (II)-(III), the L₂C₂-tank may be considered at resonance in the CRPD, and I_(L1) and I_(L2) in steady state may be found from the region (I) circuit model in FIG. 5A,

$\begin{matrix} {\begin{matrix} {{{\left( {\frac{1}{j\; \omega_{p}C_{1}} + {j\; \omega_{p}L_{1}} + R_{1}} \right)I_{L\; 1}} + V_{12}} = {V_{s}}} \\ {{{\left( {\frac{1}{j\; \omega_{p}C_{2}} + {j\; \omega_{p}L_{2}} + R_{2} + R_{M\; 1}} \right)I_{L\; 2}} - V_{21}} = 0} \end{matrix},} & (1) \end{matrix}$

where R_(M1) is the switch resistance and |V_(s)| is the amplitude of the source, V_(s). At resonance, ω_(p)=1/(L₁C₁)^(1/2)=1/(L₂C₂)^(1/2) and, therefore, the amplitude of V₂₁ in steady state may be found from,

$\begin{matrix} {{{V_{21}} = {{{V_{s}}M_{12}{\omega_{p}/\left( {R_{1} + \begin{matrix} \left( {M_{12}\omega_{p}} \right)^{2} \\ {R_{2} + R_{M\; 1}} \end{matrix}} \right)}} = {\frac{{V_{s}}k_{12}Q_{1}{\sqrt{L_{2}}/\sqrt{L_{1}}}}{1 + {k_{12}^{2}Q_{1}Q_{2\; {eq}}}} = \frac{{V_{s}}k_{12}\sqrt{Q_{1}Q_{2}}\sqrt{R_{2}}}{\left( {1 + {k_{12}^{2}Q_{1}Q_{2\; {eq}}}} \right)\sqrt{R_{1}}}}}},} & (2) \end{matrix}$

where k₁₂=M₁₂/(L₁L₂)^(1/2), Q₁=ω_(p)L₁/R₁, and Q_(2eq)=ω_(p)L₂ /(R₂+R_(M1)) is the equivalent Q of L₂ in region (I). Therefore, the Tx side may be considered as a sinusoidal source, i.e., V₂₁, in (2), in the Rx side.

In order to maximize i_(L2) and V_(R) in region (I) of FIG. 4, which may increase V_(L), one may maximize |V₂₁| in equation (2) for a given |V_(s)| since i_(L2)=|V₂₁|/(R₂+R_(M1)) in region (I). Therefore, at large distances where k₁₂ is quite small, k₁₂, Q₁, and Q₂ may be maximized, while R₂+R_(M1) may be minimized to maximize i_(L2) and, consequently V_(L).

The transient i_(L2)(t) in regions (I) and (II)-(III), which is associated with circuits in FIGS. 5a and 5b , may be found from,

$\begin{matrix} {\mspace{79mu} {{{V_{21}(t)} = {{L_{2}\frac{{di}_{L\; 2}(t)}{dt}} + {\frac{1}{C_{2}}{\int{{i_{L\; 2}(t)}{dt}}}} + {\left( {R_{2} + R_{M\; 1}} \right){i_{L\; 2}(t)}}}},}} & (3) \\ {{{{V_{21}(t)} - V_{D}} = {{L_{2}\frac{{di}_{L\; 2}(t)}{dt}} + {\frac{1}{C_{2}}{\int{{i_{L\; 2}(t)}{dt}}}} + {\frac{1}{C_{L}}{\int{{i_{L\; 2}(t)}{dt}}}} + {\left( {R_{2} + R_{D}} \right){i_{L\; 2}(t)}}}},} & (4) \end{matrix}$

respectively, where R_(D) represents the resistance of the rectifier. To find equation (4), R_(L) may be safely ignored compared to C_(L), because C_(L) may be chosen large enough to reduce the voltage ripples across R_(L). One may also ignore C_(L) in equation (4) as it is much larger than C₂ in inductive links.

The solution for i_(L2)(t) in region (I) for t₀<t<t₁ may be written as,

i _(L2)(t)=exp(α(t−t ₀))[A ₁cos(ω_(d)(t−t ₀))+A ₂ sin(ω_(d)(t−t ₀)]−A ₃ sin(ω_(p)(t−t ₀)),   (5)

where α and ω_(d) may be found from,

$\begin{matrix} {{\alpha = {- \frac{\omega_{p}}{2\; Q_{2\; {eq}}}}},{\omega_{d} = {\frac{\omega_{p}}{2\; Q_{2\; {eq}}}{\sqrt{{4\; Q_{2\; {eq}}^{2}} - 1}.}}}} & (6) \end{matrix}$

The particular solution for i_(L2), which is originated from |V₂₁| in equation (2), determines A₃, while A₁ and A₂ may be found from the initial conditions of i_(L2). Therefore, A₁₋₃ in equation (5) may be found from,

A ₁ =i _(L2)(t ₀)=0, A ₂=(−V _(C2)(t ₀)/L ₂ −αA ₁ +A ₃ω_(p))/ω_(d),   (7)

and A₃=|V₂₁|/(R₂+R_(M1)), where V_(C2) (t₀) is the initial voltage across C₂ in each switching cycle, which is the same as V_(C2) (t₃) in region (III) from the previous cycle as shown in FIG. 4. At startup, V_(C2) (t₀) in equation (7) may be set to zero. It can be seen that in order to increase i_(L2) in equation (5), A₃ may be maximized by increasing |V₂₁| in equation (2) and reducing R₂+R_(M1). This implies that k₁₂, Q₁, and Q_(2eq) may be maximized.

In region (I), C_(L) is the only source that delivers power to R_(L) and, therefore, V_(L) may slowly decrease for the amount of ΔV_(L, dec) as shown in FIG. 4. One may find ΔV_(L,dec) from,

$\begin{matrix} {{\Delta \; V_{L,{dec}}} = {{V_{L}\left( t_{0} \right)}\left( {1 - {\exp \left( \frac{{- T_{sw}} + T_{off}}{R_{L}C_{L}} \right)}} \right)}} & (8) \end{matrix}$

where T_(sw)=1/f_(sw) and T_(off)=0.25 T_(p) are the switching time period and the switch turn-off duration, respectively.

The solution for i_(L2)(t) in region (II) for t₁<t<t₂ may be found by solving equation (4) as,

i _(L2)(t)=B exp(α(t−t ₁))cos(ω_(d)(t−t ₁ )−θ)+A ₃ cos(ω_(p)(t−t ₁)),   (9)

where A₃ is almost equal to |V₂₁|/(R₂+R_(D)) for large C_(L), and

$\begin{matrix} {{B = \sqrt{\left( \frac{{{{di}_{L\; 2}\left( t_{1} \right)}/{dt}} - {\alpha \left( {{i_{L\; 2}\left( t_{1} \right)} - A_{3}} \right)}}{\omega_{d}} \right)^{2} + \left( {{i_{L\; 2}\left( t_{1} \right)} - A_{3}} \right)^{2}}},{\theta = {\tan^{- 1}\left( \frac{{{{di}_{L\; 2}\left( t_{1} \right)}/{dt}} - {\alpha \left( {{i_{L\; 2}\left( t_{1} \right)} - A_{3}} \right)}}{\omega_{d}\left( {{i_{L\; 2}\left( t_{1} \right)} - A_{3}} \right)} \right)}},{\frac{{di}_{L\; 2}}{dt} = {\frac{{V_{21}} - \left( {{V_{C\; 2}\left( t_{1} \right)} + {V_{L}\left( t_{1} \right)} + V_{D} + {\left( {R_{2} + R_{D}} \right){i_{L\; 2}\left( t_{1} \right)}}} \right)}{L_{2}}.}}} & (10) \end{matrix}$

In equation (10), i_(L2)(t₁) may be found from equation (5), and V_(C2)(t₁) is the voltage across C₂ in region (I) and may be found from,

$\begin{matrix} {{{V_{C\; 2}\left( t_{1} \right)} = {{\frac{1}{C_{2}}{\int_{t_{0}}^{t_{1}}{{i_{L\; 2}(t)}{dt}}}} + {V_{C\; 2}\left( t_{0} \right)}}},} & (11) \end{matrix}$

by using i_(L2) in equation (5). The time that i_(L2) takes in equation (9) to approach zero, i.e., t=t₂ in FIG. 4, may be approximately found from,

t ₂ −t ₁=(π/2−θ)/ω_(d),   (12)

if |V₂₁| is ignored in region (II), i.e., A₃=0, since the total stored energy in the L₂C₂-tank in region (II) is much larger than the energy provided by small V₂₁, particularly at large distances, where k₁₂ in equation (2) is relatively small.

In region (II), where i_(L2) is nonzero and the L₂C₂-tank is connected to the load, L₂ may deliver power to C_(L)∥R_(L). Therefore, V_(L) may gradually increase by discharging L₂ energy into C_(L). The amount of ΔV_(L,inc) as shown in FIG. 4 may be found from,

$\begin{matrix} {{{\Delta \; V_{L,{inc}}} = {\int_{t_{1}}^{t_{2}}{{i_{L\; 2}(t)}{{dt}/C_{L}}}}},} & (13) \end{matrix}$

by using i_(L2) in equation (9).

In region (III), the rectification diode forces 1_(L2) to remain zero, which may in turn maintain V_(C2) constant for t₂<t<t₃. Therefore, V_(C2)(t₀) in equation (7) for the next switching cycle may be found by calculating V_(C2) at t=t₃ or t₂ from,

$\begin{matrix} {{{V_{C\; 2}\left( t_{0} \right)} = {{\frac{1}{C_{2}}{\int_{t_{1}}^{t_{2}}{{i_{L\; 2}(t)}{dt}}}} + {V_{C\; 2}\left( t_{1} \right)}}},} & (14) \end{matrix}$

by using i_(L2) in equation (9). Region (III) may be added for the duration of (t₃−t₁)=T_(off)=0.25 T_(p) to ensure that L₂ is completely discharged into C_(L), which eliminates the need and power consumption for sensing the zero-crossing times of i_(L2).

TABLE I CRPD-BASED INDUCTIVE LINK PARAMETERS USED IN SIMULATIONS Parameter Value Parameter Value L₁/L₂ (μH) 205/4.2  k₁₂ 0.01 R₁/R₂ (Ω)  30/1.1 C_(L) (nF) 100 C₁/C₂ (nF) 0.123/6    R_(L) (kΩ) 100 |V_(s)| (V) 1.5 T_(off) (ns) 250 R_(D)|R_(MI) (Ω) 0/1 f_(sw) (kHz) 50 V_(D) (V) 0.4 f_(p) (MHz) 1

According to equations (8) and (13), V_(L) may decrease in region (I) and increase in region (II) for each switching cycle (T_(sw)).Therefore, the final value of V_(L) after n switching cycles may be found from,

$\begin{matrix} {{{V_{L}\left( {t = {nT}_{sw}} \right)} = {\sum\limits_{i = 1}^{n}\; \left\lbrack {{\Delta \; {V_{L,{inc}}(i)}} - {\Delta \; {V_{L,{dec}}(i)}}} \right\rbrack}},} & (15) \end{matrix}$

where ΔV_(L, dec) (i) and ΔV_(L, inc) (i) may be calculated from equations (8) and (13) for each T_(sw), respectively.

The PTE of the CRPD-based inductive link in FIG. 3 may be defined as the power delivered to R_(L), P_(L)=V_(L) ²/R_(L), divided by the power provided by V_(s), P_(s). At steady state, the final value for V_(L) may be calculated from equation (15) to find P_(L). Since the L₂C₂-tank is mostly shorted in the CRPD-based link, the link model in FIG. 5A may be used to find P_(s). In FIG. 5A, the L₂C₂-tank may be modeled in the Tx side as a reflected impedance [20],

R _(ref) =k ₁₂ ²ω_(p) L ₁ Q _(2eq) =k ₁₂ ² Q ₁ Q _(2eq) ×R ₁,   (16)

in series with R₁. Since L₁ is canceled out by C₁ at resonance, the PTE of the CRPD-based inductive link may be written as,

$\begin{matrix} {{PTE} = {\frac{V_{L}^{2}/R_{L}}{0.5{{V_{s}}^{2}/\left( {R_{1} + R_{ref}} \right)}} = {2{{\frac{V_{L}}{V_{S}}}^{2} \cdot \frac{R_{1}}{R_{L}}}{\left( {1 + {k_{12}^{2}Q_{1}Q_{2\; {eq}}}} \right).}}}} & (17) \end{matrix}$

C. Theory vs. Simulations

In order to demonstrate the functionality of the CRPD and verify the accuracy of the proposed circuit theory, the CRPD-based inductive link in FIG. 3 was simulated in the Cadence Spectre circuit simulator (Cadence Technology, San Jose, Calif.), and compared with the calculation results based on the theory. Table I summarizes the circuit parameters that were used in these simulations. The amplitude of V_(s) operating at f_(p) of 1 MHz may be set to 1.5 V to achieve V_(R) amplitude of 1 V when the M₁ was always closed. This implies that a conventional inductive link may achieve V_(L)<1 V for such settings.

FIG. 6 shows the simulated and calculated results for i_(L2), V_(R), V_(L), and the SW₁ during 50 μs of operation, when the M₁ was switched at the rate of f_(sw)=50 kHz. The circuit parameters for FIG. 6 and FIG. 7 are based on Table I. Although the peak amplitude of V_(R) (V_(R,peak)) during L₂C₂-tank energy storage (M₁: closed) is ˜1 V, V_(L) may reach to ˜1.7 V due to a sudden increase in V_(R) to >2.3 V to compensate for V_(L)+V_(D)=2.1 V, and may provide a path for discharging L₂ into C_(L). It can be seen in FIG. 6 that the calculated results match with the simulations. The slight errors in the calculated V_(L) may be due to the approximations that were made in finding the initial conditions.

FIG. 7 shows the simulated and calculated waveforms for V_(L) at f_(sw)=50 kHz, when V_(R,peak) was as small as 1 V. It can be seen that V_(L) has reached to ˜3.7 V in steady state, which results in an AC-DC VCE of 3.7 due to the optimal control of the SW₁ in the CRPD. FIG. 7 inset also shows the ripples on V_(L) in steady state, in which ΔV_(L, dec) and ΔV_(L, inc) in equation (15) have cancelled out each other.

As shown in FIG. 7, the rate of increase in V_(L) is relatively faster at the startup, where V_(L) is relatively small, because 1) according to equation (8), ΔV_(L,dec) is proportional to V_(L) and, therefore, ΔV_(L,dec) is quite small at low V_(L), and 2) ΔV_(L,inc) in equation (13) is proportional to i_(L2) values within t₁<t<t₂, which decay at a lower rate at low V_(L), where the voltage on L₂ is smaller and, therefore, ΔV_(L,inc) is larger at low V_(L). However, as V_(L) increases, ΔV_(L, dec) may increase and ΔV_(L, inc) may decrease, until they become equal, resulting in a steady-state value for V_(L).

IV. Design Procedure for Proposed CRPD-Based Inductive Link

In order to maximize VCE and PTE of the CRPD-based inductive link, the power loss in both Tx and Rx sides may be minimized. In the Rx side, the optimal f_(sw) may ensure that V_(L) and consequently P_(L)=V_(L) ²/R_(L) may be maximized for a given V_(R), leading to higher VCE and lower power loss in Rx. As shown in Section III. A, the amount of rectifier voltage drop (V_(D)) and R₂+R_(M1) may be minimized to increase V_(L). Since the L₂C₂-tank is mostly shorted in the CRPD-based link, the link model in FIG. 5a may be used to find the power loss in the Tx side. By modeling the L₂C₂-tank in the Tx side with R_(ref) in equation (16), the power efficiency in the Tx side may be found from,

η_(Tx) =R _(ref)/(R ₁ +R _(ref))=k ₁₂ ² Q ₁ Q _(2eq)/(1=k ₁₂ ² Q ₁ Q _(2eq)).   (18)

Since the proposed CRPD may enable extended-range inductive power transmission, the Tx and Rx coils are weakly coupled at large distances and, therefore, k₁₂ may be relatively small. In this condition, η_(Tx) may be simplified to k₁₂ ²Q₁Q_(2eq). Therefore, the proposed design procedure in FIG. 8 may include two parts, 1) maximizing k₁₂ ²Q₁Q_(2eq) by optimizing L₁ and L₂ geometries to reduce the power loss in the Tx side, and 2) reducing V_(D) and R_(M1), and optimizing f_(sw) to increase V_(L). It may be noted that maximizing k₁₂ ²Q₁Q_(2eq) may also increase V_(R) and V_(L) at large distances, because i_(L2) in equation (7) may depend on A₃, which may be simplified to

$\begin{matrix} {{A_{3} = {\frac{V_{21}}{R_{2} + R_{M\; 1}} = {\frac{{V_{s}}k_{12}Q_{1}{\sqrt{L_{2}}/\sqrt{L_{1}}}}{R_{2} + R_{M\; 1}} = \frac{{V_{s}}k_{12}Q_{1}Q_{2\; {eq}}}{\omega_{p}\sqrt{L_{1}L_{2}}}}}},} & (19) \end{matrix}$

where k₁₂ is considered small.

Reference [20] shows that at short distances, which involve large k₁₂, the optimal geometries for Tx and Rx coils that may maximize V_(L) and PTE can potentially be different. Tx and Rx coils geometries can be optimized to maximize η_(Tx) in equation (18) using the design procedure that has been presented in reference [20]. However, at large distances a single set of Tx and Rx coils geometries may maximize both V_(L) and PTE. Therefore, in the CRPD that is suitable for large distances, maximizing V_(L) based on the design procedure in FIG. 8 may also lead to maximum PTE.

A designer may make the coils as lithographically defined or wire-wound. The geometrical parameters of the printed spiral coils (PSC) that affect circuit parameters such as Q and k are the line width (w), line spacing (s), outer diameter (D_(o)), and fill factor (φ: the ratio between the difference and the sum of a PSC' s inner and outer diameters), which have been described in reference [6]. In wire-wound coils (WWC) made of single filament solid wires, w is the wire diameter, the number of turns (n: integer) may be used instead of φ, and s may be twice the thickness of the wire insulation. The relationship between circuit parameters and the coil geometries in this case may be found in reference [21].

In step-1 100 of the design procedure in FIG. 8, design constraints imposed by the application and coil fabrication technology may be considered. The former may define the maximum value for Rx coil diameter, D_(o2), while the latter may indicate the minimum line width and line spacing (w_(min), s_(min)) in the case of PSC, or the wire specifications in WWC. The nominal values for coupling distance (d₁₂), R_(M1), and R_(L) are also required in this step, which are application dependent on the application.

In step-2 200, the initial values for L₁ and L₂ geometries may be chosen, including (w_(1,2), w_(1,2), φ_(1,2), D_(o1)) and (w_(1,2), s_(1,2), n_(1,2), D_(o1)) for PSCs and WWCs, respectively. A detailed discussion about how to choose initial values can be found in references [6] and [20]. In step-3 300, the geometries of L₁ and L₂ may be optimized to maximize k₁₂ ²Q₁Q_(2eq) based on the iterative design procedure that is presented in reference [20] using k and Q equations for PSCs and WWCs in references [6] and [21], respectively. This involves sweeping different parameters of L₁ and L₂ in an iterative process and finding the maximum value for k₁₂ ²Q₁Q_(2eq) in each step, which has been discussed in references [6], [20], and [21].

In step-4 400, f_(sw) may be swept to find the final value for V_(L) in equation (15) for |V_(s)|=1 V using the optimal coil geometries from step-3 300. The optimal f_(sw) that maximizes V_(L) may be chosen in this step. Step-4 400 may determine optimal coil geometries and f_(sw) to achieve highest V_(L) and PTE in the CRPD, which may be further validated and fine-tuned through simulations and measurements in step-5 500. Thus, the design procedure concludes at the end of step-5 500.

V. VCIPM Chip Architecture

FIG. 9 shows the block diagram of a prototype VCIPM chip, which was designed at the f_(p) of 1 MHz to regulate V_(L) at V_(DD)=3.2 V. The VCIPM chip operates in either VM or CM based on the V_(R) amplitude using M₂ or M₁ and M₃ transistors, respectively, and performs rectification, regulation, and OVP all in one step with a single off-chip capacitor (C_(L)). In VCIPM chip, a passive envelope detector first detects V_(R) amplitude. Then, a mode selection (MS) block determines whether VCIPM chip should operate in VM (if V_(R)>3.2 V) or CM (if V_(R)≦3.2 V) by enabling voltage-mode controller (VMC) or current-mode controller (CMC) blocks, respectively. If VMC is enabled, M₁ (W/L=2.5 mm/0.6 μm) is turned on by setting SW₁=3.2 V, and M₂ (W/L=0.5 mm/0.6 μm) is controlled by SW₂ to form a half-wave active rectifier as shown in FIG. 2. In VM, diode-connected M₃ (W/L=10 mm/0.6 μm) is always off, because its source-gate voltage is negative. If CMC is enabled, M₂ is turned off by setting SW₂=3.2 V, and M₁ is controlled by SW₁ as shown in FIG. 4. Self-regulation will also be achieved in VMC and CMC by adjusting SW₂ and SW₁ pulses, respectively. A bandgap reference (BGR) provides a constant 1.2 V, from which a reference bias current of 60 nA is generated by a current generator (CG).

FIGS. 10A and 10B show the block diagrams and key operational waveforms of VMC and CMC, respectively. In VMC, a regulation amplifier (Reg_Amp in FIG. 10a ), controlling the bias current (I_(bias)) of the active rectifier comparator (VM_Comp), amplifies the difference between V_(L) and required V_(DD)=3.2 V by comparing 0.37×V_(L) with V_(BGR)=1.2 V. If V_(L)<3.2 V, this amplifier outputs low and I_(bias) is maximized. Therefore, VM_Comp operates at its maximum speed with minimal back current, i.e., as an efficient active rectifier, to charge C_(L) and increase V_(L). When V_(L) surpasses 3.2 V, Reg_Amp reduces I_(bias), slowing down CM_Comp in turn-off, that allows back current from C_(L) to L₂C₂-tank by increasing the width of SW₂ pulses (T_(d) in FIG. 2), as it can be clearly seen in FIG. 10a inset waveforms.

In CMC as showing in FIG. 10B, a time-base generator (TBG), whenever it is reset, outputs a high pulse after 4 μs to enable a regulation comparator (Reg_Comp) that compares 0.37×V_(L) with V_(BGR)=1.2 V. If V_(L)<3.2 V, the CM comparator (CM_Comp) with an intentional offset of 170 mV is enabled by Reg_Comp to detect the time zero-crossings of V_(R), where i_(L2) reaches its maximum, with the help of a synchronization block and consequently generates a sharp SW₁ pulse to charge C_(L) through M₃. The synchronization block includes two cascaded D-flip-flops that count two pulses to generate a transition, which is then converted to a short pulse (active low) with the width of T_(p)/4 by a pulse generator block. The pulse-generator output controls M₁ with a driver (SW₁ pulses), and also resets D-flip-flops and TBG for the same process to be repeated. FIG. 10b inset shows how synchronization block can eliminate false CM_Comp pulses, which are not at the time zero-crossings of V_(R). The intentional offset in CM_Comp compensates for the circuit delays in CMC path, ensuring M₁ switching occurs at i_(L2) peaks. If V_(L)>3.2 V, CM_Comp is disabled and, therefore, SW₁ remains high and C_(L) is not charged. It can be seen that f_(sw) is automatically adjusted to regulate V_(L) at 3.2 V. The maximum f_(sw) is limited to 166.6 kHz in VCIPM chip according to CRPD theory in the previous sections.

VI. Measurement Results

Two sets of measurements have been made to prove the functionality of CRPD and VCIPM techniques. First, a proof-of-concept CRPD-based inductive link was designed using PSCs and its measured performance was compared with that of a conventional inductive link. In addition, an ASIC implementation of the VCIPM chip was done in a 0.35 μm standard CMOS process, and its operation in VM and CM was examined.

Table II below shows the geometries of Tx and Rx coils as well as circuit parameters that were used in CRPD measurement. The inductive link was designed at f_(p) of 1 MHz to power a nominal R_(L) of 100 kΩ at the nominal distance of d₁₂=7 cm. The diameter of the Rx coil was limited to D_(o2)=3 cm. The same set of Tx and Rx coils were used for both CRPD-based and conventional links.

FIG. 11 shows the CRPD measurement setup that includes Tx and Rx coils, designed on FR4 printed circuit boards (PCBs), and a custom-designed discrete circuit for switching the L₂C₂-tank based on the optimal switching scheme in FIG. 4. The coil geometries and circuit parameters can be found in Table II. The setup block diagram has also been shown in FIG. 11 inset. In this proof-of-concept setup, a discrete transistor and diode with nominal R_(M1) of 0.2Ω and V_(D) of 0.3 V at the forward current of 10 mA were used, respectively. A function generator provided two synchronous signals to drive L₁ at f_(p) of 1 MHz and the switch at adjustable f_(sw). For the sake of comparison, the measurement setup was slightly modified to realize

TABLE II COILS GEOMETRIES AND CIRCUIT PARAMETERS IN MEASUREMENTS FOR CRPD-BASED AND CONVENTIONAL INDUCTIVE LINKS Parameters Symbols CRPD Conventional L₁ Inductance (μH) L₁ 250 Outer diameter (mm) D_(o1) 170 Fill factor φ₁ 0.4 Number of turns n₁ 35 Line width (mm) w₁ 1.2 Line spacing (mm) s₁ 0.2 Quality factor Q₁ 62.5 L₂ Inductance (μH) L₁ 4.4 Outer diameter (mm) D_(o2) 30 Fill factor φ₂ 0.55 Number of turns n₂ 14 Line width (mm) 0.6 Line spacing (mm) s₂ 0.2 Quality factor Q₂ *24.2 29 L₁-L₂ coupling distance (mm) d₁₂ 70 Operation frequency (MHz) f_(p) 1 Nominal load resistance (kΩ) R_(L) 100 Load capacitance (nF) C_(L) 100 Source voltage (V) |V_(s)| 0.39 Received voltage (V) |V_(R)| 1 1.05 Load voltage (V) V_(L) 3.1 0.95 Switching frequency (kHz) f_(sw) 50 — Voltage conversion efficiency VCE 3.1 0.9 PTE (%) η 5.3 0.45 *Q₂ in CRPD link also includes R_(MI) of 0.2 Ω. conventional inductive link, followed by a passive rectifier with similar diode and C_(L)∥R_(L) as shown in FIG. 1.

FIG. 12 shows the measured waveforms for the CRPD, including from top: V_(L), V_(R), and SW₁, when the inductive link was operating at f_(p)=1 MHz and d₁₂=7 cm with f_(sw)=50 kHz. As can be seen in FIG. 12A, V_(L) across R_(L) and C_(L) of 100 kΩ and 100 nF increased for ˜20 mV at each switching cycle of 20 μs, respectively. As shown in FIG. 12b , V_(L) reached to 3.1 V within ˜30 ms after the switching started, when the maximum amplitude of the received voltage, |V_(R)|, was only 1 V, leading to high VCE of 3.1 due to the CRPD. As shown in FIG. 12B inset, when the SW₁ was opened every 20 μs, V_(R) suddenly jumped to ˜3.4 V, which was higher than V_(L) of 3.1 V, to provide a path for L₂ to be discharged into the load. It should be noted that the amplitude of V_(R) was very small when SW₁=0, i.e., switch was opened for a long time, because the series connected L₂C₂-tank was heavily loaded by R_(L) of 100 kΩ. In all measurements, the SW₁ was increased to 4 V to reduce the discrete switch resistance (R_(M1)). However, in another embodiment of the integrated CRPD, a low-voltage large transistor with small R_(M1) may be used.

FIG. 13 shows V_(L) and PTE of the CRPD-based inductive link vs. f_(sw) for the R_(L) of 100 kΩand |V_(s)| of 0.39 V at d₁₂=7 cm. It can be seen that at the optimal f_(sw) 50 kHz, maximum V_(L) and PTE of 3.1 V and 5.3% may be achieved, respectively. For f_(sw) much greater than 50 kHz, the L₂C₂-tank cannot store maximum energy and, therefore, i_(L2) and V_(R) in FIG. 3 may be small, resulting in low V_(L) values. For f_(sw) much smaller than 50 kHz, the L₂C₂-tank is shorted for a long period, and more energy may be wasted into the L₂C₂-tank (R₂+R_(M1)), resulting in low V_(L) again. It should be noted that |V_(s)| was measured at the input of the inductive link, as shown in FIG. 11 inset, to eliminate the effects of signal generator output impedance in the measurements. For the same conditions, the conventional inductive link may achieve V_(L) and PTE of 0.95 V and 0.45%, respectively. Therefore, the proposed CRPD-based inductive link may increase V_(L) and PTE by ˜3.3 and 11.8 times, compared to the conventional inductive link, respectively.

FIGS. 14A and 14B show V_(L) and PTE vs. R_(L) for both CRPD-based and conventional inductive links at d₁₂=7 cm and |V_(s)|=0.39 V, as well as the optimal f_(sw) to maximize V_(L) and PTE at each R_(L), respectively. For the CRPD link, the optimal f_(sw) at each R_(L) was found in the measurements, and then V_(L) and PTE were measured at each R_(L) with the corresponding f_(sw). It can be seen that the proposed CRPD may significantly improve V_(L) and PTE for R_(L) values larger than 5 kΩ. It can be seen in FIGS. 14a and 14b that for small R_(L), which may demand more current from C_(L), the optimal f_(sw) may be increased to charge C_(L) more frequently. However, for large R_(L) the optimal f_(sw) may be decreased to provide more time for the L₂C₂-tank to reach to its maximum energy. It can be seen in FIGS. 14a and 14b that the same f_(sw) can maximize both V_(L) and PTE. The CRPD-based link achieved higher V_(L) and consequently PTE for R_(L)≧10 kΩ with the optimal f_(sw)s of 50-100 kHz. However, the conventional link was superior for R_(L)<5 kΩ, at which the equivalent resistance of the parallel-connected L₂C₂-tank was matched to R_(L). In CRPD, AΔV_(L, dec) in equation (8) may be significantly increased for small values of R_(L), and limited V_(L). Nonetheless, the proposed CRPD-based link may achieve higher V_(L) and PTE for a wide range of R_(L).

In measurements, in order to synchronize SW₁ with the peak of i_(L2) as shown in FIG. 4, the zero-crossing times of V_(R) were observed, because when the SW₁ is closed and V_(R)=0, the maximum energy is stored in L₂, which is equivalent to i_(L2) peaks. It should also be noted that for the same conditions, the conventional inductive link followed by the same passive rectifier achieved |V_(R)| and V_(L) of 1.05 and 0.95 V, leading to the small VCE of 0.9. In the conventional inductive link, |V_(R)| was slightly higher than that of CRPD, because L₂ was not loaded by R_(M1) of 0.2 Ω and, therefore, Q₂ was higher.

It should be noted that based on FIGS. 14A and 14B, the proposed CRPD may be suitable for applications that either involve low-power consumption in the Rx side, i.e., large R_(L), such as RFID and low-power IMDs, or require a duty-cycled high-power and high-voltage Rx, in which a large capacitor (C_(L)) is often charged through the inductive link and then discharged on a small R_(L). As an example, FIG. 14a shows that V_(L) of 7.1 V may be achieved for the large R_(L) of 1 MΩ, while |V_(R)| was as small as 1 V, leading to the VCE of 7.1.

FIG. 15 shows the measured values of V_(L) vs. d₁₂ for the CRPD-based and conventional inductive links for R_(L) of 100 kΩ. FIG. 15 also shows the optimal values of f_(sw) for the CRPD link at each distance. As the distance is increased from 1 cm to 15 cm, the optimal f_(sw) reduces from 100 kHz to 50 kHz. In these measurements, |V_(s)| was increased to 1.05 V to achieve a minimum V_(L) of 2.8 V at d₁₂=7 cm in the conventional inductive link, which may be further regulated to 2.5 V. As shown in FIG. 15, the proposed CRPD could extend the powering distance to 13 cm to achieve the minimum V_(L) of 2.8 V for the same |V_(s)| of 1.05 V. It should be noted that V_(L) was reduced for d₁₂<5 cm in both links, because the reflected load in equation (16) was increased at short distances, which reduced the available P_(s). Therefore, |V_(s)| can be safely increased at short distances to increase V_(L) to 2.8 V in the conventional inductive link with a much smaller P_(s) compared to d₁₂>5 cm, since PTE is much higher at short distances.

TABLE III BENCHMARKING OF RECENT EXTENDED-RANGE INDUCTIVE POWER TRANSMISSION LINKS Parameters 2015, [33] 2017, [39] 2016, [34] CRPD Tx/Rx Series/ Series/ Series/ Series/ Resonance Series Series Series Series V_(R) (V) *5.5 *25   4.8 1 V_(L) (V) 4.5 20   4.22 3.1 R_(L) (kΩ) 0.2  0.02 0.5 100 f_(p) (MHz) 2  0.2 13.56 1 f_(sw) (MHz) 4 — 2.28 0.05 VCE 0.82  0.8 0.88 3.1 *Calculated from FIGURES in the paper.

FIG. 16 shows the measured V_(L) of the CRPD-based and conventional inductive links vs. |V_(R)| for the R_(L) of 100 kΩ, d₁₂ of 7 cm, and f_(sw) of 50 kHz. In these measurements, |V_(s)| was swept to achieve these |V_(R)| and V_(L) values. For a wide range of |V_(R)| from 0.3-3.5 V, the proposed CRPD may achieve a higher V_(L) and consequently VCE. As can be seen in FIG. 16, the CRPD may increase V_(L) to ˜14 V for |V_(R)| of 3.5 V, i.e., VCE=4, which shows that the proposed CRPD may be suitable for applications that require high voltage in the Rx side. Thus, the CRPD significantly increased V_(L) for different |V_(R)| values as compared with the conventional link. Some embodiments of the present invention may increase V_(L) beyond 14 V and/or the powering distance may be increased over 13 cm. In accordance to some embodiments, the L₂C₂-tank may be operable to deliver energy to the loads having different R_(L).

Table III benchmarks the proposed CRPD against recent extended-range inductive power transmission links for direct powering of a load. The proposed CRPD may offer a higher VCE for a large R_(L) with adding a single switch, which can be easily integrated on a chip. Compared to the prior art, higher VCE has been achieved in the CRPD by creating a jump on the Rx coil voltage.

The following discussion presents the VCIPM chip measurement results. The VCIPM chip was fabricated in a 0.35 μm 2P4M standard CMOS process, occupying 1.56 mm² and 0.52 mm² with and without pads as shown in FIG. 17, respectively. Inductive coil geometry is the same as CRPD measurement set up, as shown in FIG. 11. In Tx, a signal generator was used to drive L₁ at f_(p)=1 MHz. In Rx, the L₂C₂-tank was connected to the VCIPM chip to achieve a regulated V_(L) of 3.2 V across C_(L)=2 μF for different conditions.

FIGS. 18A and 18B show the measured V_(L) and V_(R) waveforms with different time scales in VM at R_(L)=100 kΩ when the Tx voltage (V_(s) in FIG. 11) was increased from 11 V to 15 V peak-to-peak, demonstrating that despite V_(s) increase, the VCIPM chip adaptively adjusted the width of SW₂ pulses to regulate V_(L) at 3.2 V. As shown in FIG. 18a , since the Rx LC-tank received more power at V_(s)=15 V_(p-p), VCIPM chip employed back current more frequently, seen as sudden decreases in V_(R), to regulate V_(L). Since V_(R,peak) was higher than 3.2 V, the chip automatically operated in VM. It should also be noted that due to the proposed back-current regulation, V_(R) amplitude was maintained fairly constant despite V_(s) increase.

FIGS. 19A and 19B show the measured V_(L) and V_(R) waveforms with different time scales in CM at R_(L)=100kΩ when V_(s) was increased from 4 V_(p-p) to 9 V_(p-p), demonstrating that for V_(s)=4 V_(p-p) (1) since V_(R,peak) was 1.2 V in steady state without switching (<V_(DD)=3.2 V), the chip automatically operated in CM, and (2) V_(R) jumped from 1.2 V to ˜5 V by turning M₁ off with proper SW₁ pulses to charge C_(L) to 3.2 V. Despite V_(s) increase to 9 V_(p-p), in which V_(R,peak) increased to 2.9 V (still below 3.2 V), the VCIPM chip remained in CM configuration and adaptively adjusted f_(sw) to regulate V_(L) at 3.2 V. As shown in FIG. 19B, at lower V_(s) of 4 V_(p-p), resulting in less power delivered to Rx, the chip generated SW₁ pulses at the highest f_(sw) of 166.6 kHz to more frequently charge C_(L). In contrast, at higher V_(s) of 9 V_(p-p) with increased received power, f_(sw) was automatically decreased to charge C_(L) less frequently and regulate V_(L) at 3.2 V. It should be noted that the proposed VCIPM chip achieved a high VCE of 2.7 V/V at V_(s)=4 V_(p-p). Nonetheless, the maximum measured VCE in VCIPM chip was 3.55 V/V at f_(sw)=166.6 kHz, R_(L)=100 kΩ,V_(L)=3.2 V, and steady state V_(R,peak) of 0.9 V.

FIG. 20 shows automatic reconfiguration of the VCIPM chip from CM to VM when V_(s) was suddenly increased from 4 V_(p-p) to 10 V_(p-p) in measurements with R_(L)=100 kΩ. At lower V_(s)=4 V_(p-p), the steady-state V_(R,peak) was 1.2 V and, therefore, the chip operated in CM to regulate V_(L) at 3.2 V by large V_(R,peak) of ˜5 V, i.e., operating with high VCE of 2.7 V/V. As V_(s) was increased to 10 V_(p-p), V_(R,peak) was gradually increased to 3.3 V after ˜15 μs (higher than required V_(DD) of 3.2 V), in which the VCIPM chip automatically changed its configuration to VM. FIG. 20 clearly shows that V_(L) remained constant at 3.2 V for a drastic change in V_(R) amplitude.

VII. Conclusion

A new power management has been presented for inductive power delivery that is able to work in both VM and CM adaptively. An ASIC implementation, and measurement results of a reconfigurable voltage- and current-mode power management with self-regulation for inductive power transmission is presented to operate in optimal configuration for different cases. The VCIPM chip could achieve high VCE and PCE by operating in current and voltage modes, respectively. In VCIPM chip, adjusting back current in VM and f_(sw) in CM, regulation and OVP could be achieved along with rectification, eliminating the need for two off-chip capacitors.

In another measurement set up, CRPD technique is examined separately. The receiver LC-tank may be switched every several power carrier cycles to store energy in the LC-tank and then deliver it to the load within a quarter of the power carrier cycle by connecting the receiver LC-tank in series with a rectifier, which drives the load capacitor and resistor. Since the receiver LC-tank has been used as a current source, a large AC-DC voltage conversion efficiency may be achieved. Measurement results have shown that the proposed technique may increase the output of a conventional inductive link, followed by a passive rectifier. In a proof-of-concept measurement setup, the proposed technique could increase the rectifier output by 3.3 times from 0.95 V to 3.1 V across a load of 100 kΩ, by switching the receiver LC-tank at 50 kHz. These measurements have validated that the proposed current-based resonant power delivery technique may be suitable for extending the range of inductive power transmission for applications that involve receivers with low-power consumption and high voltage.

It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention covers the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents. The entire content of the following articles are herein incorporated by reference in their entirety.

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1. A current-based resonant power delivery device for inductive power transmission to a load, comprising: a transmitter coil; a receiver circuit, the receiver circuit having a receiver coil, a resonance capacitor, a switch, a rectification device, and a load capacitor; and the transmitter coil configured to energize the receiver coil, the receiver coil connected to the load via the resonance capacitor and the rectification device, the switch having a first state and a second state, the receiver circuit configured to build up and transfer energy between the receiver coil and the resonance capacitor by bypassing the load during the first state of the switch, the receiver circuit further configured to transfer energy from the receiver coil to the load during the second state of the switch.
 2. The current-based resonant power delivery device of claim 1, wherein the rectification device comprises a diode.
 3. The current-based resonant power delivery device of claim 1, wherein the switch remains in the first state for a plurality of power carrier cycles until the receiver coil reaches a desired receiver coil current and then the switch transitions from the first state to the second state, the switch remains in the second state for one-quarter of a power cycle, and returns to the first state for the plurality of power carrier cycles.
 4. The current-based resonant power delivery device of claim 1, wherein the switch having an adjustable switch frequency, the switch transitioning from the first state to the second state and vice versa.
 5. The current-based resonant power delivery device of claim 1, wherein the receiver coil and the resonance capacitor are connected in a series connection, the switch connected in parallel with the series connection, and the rectification device connected between the resonance capacitor and the load.
 6. The current-based resonant power delivery device of claim 3, wherein the switch is transitioning between the first state and the second state at a switching frequency to maintain the load about a desired voltage.
 7. A current-based resonant power delivery method for inductive power transmission to a load, comprising the following steps: providing a current-based resonant power delivery device of claim 1; energizing the transmitter coil; selecting the first state of the switch for building up and transferring energy between the receiver coil and the resonance capacitor for a predetermined time; and selecting the second state of the switch for transferring energy from the receiver coil to the load after the pre-determined time.
 8. The current-based resonant power delivery method of claim 7, further comprising: connecting the receiver coil and the resonance capacitor to each other in a series connection; connecting the switch in parallel with the series connection; and connecting the rectification device between the capacitor and the load.
 9. A self-regulated resonant voltage/current mode method power delivery device for inductive power transmission to a load, comprising: a transmitter coil; a receiver circuit, the receiver circuit having a receiver coil, a resonance capacitor, a first switch, a second switch, a rectification device, and a load capacitor, the transmitter coil configured to energize the receiver coil; and a mode selection circuit operable to select a voltage mode or a current mode based on a voltage across the receiver coil and a desired load voltage across the load, the mode selection circuit selecting the voltage mode when the desired load voltage is less than the receiver coil voltage and the mode selection circuit selecting the current mode when the desired load voltage is more than the receiver coil voltage, the receiver coil connected to the load via the first switch, the first switch configured to maintain the load about the desired load voltage by employing back current during the voltage mode, the receiver coil further connected to the load via the resonance capacitor and the rectification diode, wherein the second switch is connected from the resonance capacitor to the ground, the second switch having a first state and a second state, the receiver circuit configured to build up and transfer energy between the receiver coil and the resonance capacitor by bypassing the load during the first state of the second switch during the current mode, the receiver circuit further configured to transfer energy from the receiver coil to the load during the second state of the second switch when a desired energy is stored in the receiver coil during the current mode, the second switch configured to maintain the load about the desired load voltage by adjusting its switching frequency during the current mode.
 10. The self-regulated resonant voltage/current mode method power delivery device of claim 9, wherein the first switch is transitioning between an ON state and an OFF state at a first switching frequency.
 11. The self-regulated resonant voltage/current mode method power delivery device of claim 10, wherein the first switch is employing back current during the ON state.
 12. The self-regulated resonant voltage/current mode method power delivery device of claim 9, wherein the second switch is transitioning between the first state and the second state at a second switching frequency.
 13. The self-regulated resonant voltage/current mode method power delivery device of claim 9, wherein the receiver coil and the resonance capacitor are connected in a series connection, the second switch connected in parallel with the series connection, and the rectification device connected between the resonance capacitor and the load.
 14. The self-regulated resonant voltage/current mode method power delivery device of claim 9, wherein the rectification device comprises a third switch and the receiver circuit is configured to transfer energy from the receiver coil to the load through the third switch during the second state of the second switch.
 15. The self-regulated resonant voltage/current mode method power delivery device of claim 10, further comprising a voltage mode controller, the voltage mode controller regulating the first switching frequency to maintain the load about the desired load voltage.
 16. The self-regulated resonant voltage/current mode method power delivery device of claim 12, further comprising a current mode controller, the current mode controller regulating the second switching frequency to maintain the load about the desired load voltage. 